41. Eratosthenes--References eratosthenes of cyrene. University of Utah. Cited January 25, 2002. Eratosthenesof Cyrene. O Connor, JJ, and Robertson, EF Cited January 25, 2002. http://www.albertson.edu/math/History/emacy/Classical/references.htm

ACI Math Department Eratosthenes of Cyrene (276-194 b.c.) Eratosthenes biography historical setting discovery ... Math History References and Interesting Links Eratosthenes of Cyrene. University of Utah. Cited January 25, 2002. http://www.math.utah.edu/~alfeld/Eratosthenes.html Encyclopedia.com. Electric Library. Cited January 25, 2002 http://www.encyclopedia.com/articles/04184.html This link has a diagram showing the manner in which Eratosthenes measured the circumference of the earth. http://astrosun.tn.cornell.edu/courses/astro201/eratosthenes.html Follow this link for an experiment for high school geometry students. This site gives detailed instructions in how to proceed with a cooperative effort among school. Use of satellite uplinks is recommended in order to share results in real time. http://math.rice.edu/~ddonovan/Lessons/eratos.html Eratosthenes of Cyrene. O'Connor, JJ, and Robertson, E. F. Cited January 25, 2002. The picture on the left and throughout this site comes from this article. http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Eratosthenes.html

42. Online Book rotate around a stationary Earth. eratosthenes of cyrene Eratosthenesof Cyrene (ca. 284ca. 192 BC) Among Eratosthenes accomplishments http://www.cox-internet.com/ast305/all1.html

Ancient Astronomy A Brief Introduction to Archaeoastronomy The study of the astronomical practices, celestial lore, mythologies, religions and world-views of all ancient cultures we call archaeoastronomy. America's Stonehenge Along with it's astronomical alignments, America's Stonehenge continues to be one of the most fascinating archaeological discoveries of the century. Ancient Astronomy Links Some selected links to pages with information on Ancient Astronomy Calendars and Ancient Astronomy in Egypt, India, Maya, and Mesopotamia. Ancient Astronomy Timeline A timeline of ancient astronomy from 4000 B.C. to around 140 A.D. Ancient Mesopotamia: Astronomy and Calendry Part of a history of astronomy course with links to photographs and explanations. Babylonian Planetary Theory and the Heliocentric Concept Gathered ideas regarding the view of the cosmos by ancient Babylonians as well as new interpretations are on display here. With data on periods and planetary motions. Chinese Astronomy Astronomy truly is an ancient science in China. In fact, mankind's first record of an eclipse of the Sun was made in China in 2136 BC. Egyptian Estimates of the Size and Shape of the Earth How did ancient Egyptians measure the size of the Earth?

43. ORIENTALIA | Encyclopedia | Cultural Studies: Philosophy And Psychology | Eratos Eratosthenes 1995. 9. Books eratosthenes of cyrene. Price Not availableSubject to change. eratosthenes of cyrene by PM Fraser 1971. page http://www.orientalia.org/term25321.html

This is an academic Eastern Philosophy and Religion site! Please, register to access all sections. Navigator Home Account New Password Site Map ... Feedback User Info Welcome, Guest Nickname Password Security Code: Type S-Code: Register Membership: Latest: liane New Today: New Yesterday: Overall: People Online: Visitors: Members: Total: Forums Last 20 Forum Messages Have you heard of the name David Ecke? ..... Last post by Guest in Feadback and Support on May 30, 2004 at 07:55:15 two words in sanskrit Last post by Guest in Teach Me on May 27, 2004 at 15:10:14 Continental Philosophy Last post by Guest in Comparative Philosophy on May 25, 2004 at 20:48:46 Corrupt Zip Files Last post by Plamen in Googlifier on May 13, 2004 at 18:26:18 The Dao of the Press Last post by Plamen in Technology of Wisdom on May 04, 2004 at 04:28:51 Cakra- Mooney Last post by Guest in Round Table on Apr 29, 2004 at 17:15:27 Save the Earth! Last post by Guest in Buddhist Studies on Apr 27, 2004 at 09:20:50 SVARA Last post by Plamen in Teach Me on Apr 20, 2004 at 17:28:39 Here and Now Last post by Plamen in Buddhist Studies on Apr 20, 2004 at 14:37:00

44. February 2004 Web Sites quantitiy. eratosthenes of cyrene ( 6 - 12 ) - A versatile scholar,eratosthenes of cyrene lived approximately 275-195 BC. He http://members.shaw.ca/dbrear/February2004websites.html

February 2004 Web Sites The following Web sites looked interesting : From the magazine, Teaching Pre K - 8 February 2004 Topic : Hot Websites PBS KIds Democracy Project - the three main interactive areas of this site put students in a decision-making simulation that leads them to investigate the US government, the presidency and voting. The Science Spot - this site has everything you might need for the science curriculum. Cool Science for Curious Kids - investigating science is easy with this interactive site. Using Live Insects - Using Live Insects in Elementary Classrooms for Early Lessons in Life, funded by the National Institutes of Health Science Education Partnership Award, is a program dedicated to introducing health topics to children in kindergarten through third grade. The Amazing Human Body - is a resource that will engage students in scientific inquiry and enhance their knowledge of their body systems. Topic : Internet Internet 101 for students, learn all about the Internet, Email and the WWW. Email Tutorials - great source for Email tutorials.

45. Eratosthenes From HistoryCenter.net eratosthenes of cyrene studied in Alexandria and Athens. In Alexandriahe was director of the great library. This scholar of natural http://www.historycenter.net/science-detail1.asp?ID=8&TimeZone=5

46. Astronomy eratosthenes of cyrene Astronomy OnLine Eratosthenes Project - this project invitesyou to measure the circumference of the Earth, in a collaboration with http://www.cannylink.com/astronomy.htm

Astromony Education Books Computers Homework ... X-Ray Astronomers Brahe, Tycho (1546-1601) Brahe Brahe, Tycho Noble Dane: Images of Tycho Brahe Tycho Brahe - biography of the astronomer from Rice University. Tycho Brahe Danish Astronomer Tychonides Bruce Medalists - brief biographies of astronomers awarded the Bruce Medal of the Astronomical Society of the Pacific since 1898. Copernicus, Nicolaus (1473-1543) Copernican Model: A Sun-Centered Solar System Copernican Revolution Copernican System Copernicus, Nicolaus - The Catholic Encyclopedia ... Copernicus, The Revolutions - dedication of the revolutions of the heavenly bodies. Monument to Copernicus - work in progress. Nicolaus Copernicus Scientists: Nicolas Copernicus Web Directory: Copernicus Links Deep Skies - general information about some astronomers and space travel related physics. Eratosthenes of Cyrene Astronomy On-Line: Eratosthenes Project - this project invites you to measure the circumference of the Earth, in a collaboration with other Astronomy On-Line groups. Eratosthenes of Cyrene - from Dr. Peter Alfeld of the University of Utah.

47. WHKMLA : Era Of Discovery, Flat Earth Versus Round Globe be flat. Actually, eratosthenes of cyrene, head of the Great Libraryof Alexandria had proven the earth to be round. Knowing that http://www.zum.de/whkmla/period/disc/flatearth.html

Flat Earth versus Round Globe The Bible contains a statement expressing the earth to be flat. Actually, Eratosthenes of Cyrene, head of the Great Library of Alexandria had proven the earth to be round. Knowing that on a certain day, at noon, an obelisk in Luxor (s. Egypt) would cast no shadow, at exactly the same time he measured the shadow of an obelisk in Alexandria. He knew the height of the obelisk and the distance between Alexandria and Luxor; the rest is trigonometry. Claudius Ptolemy's geography is also based on the concept of the earth being round, and sun, moon and the stars circling around the earth. During the Renaissance, Greek texts were rediscovered, among them Eratosthenes' calculation and Ptolemy's geography. Yet to openly state the earth to be round would be to contradict the bible, which, in its entirety, was believed to be the word of God. A person who postulated the earth to be round was a case for the inquisition. Popular concept had it, that at the fringes of the earth people would fall down into the depth of hell. However, the campaigns of Alexander (to India), of Marco Polo and others (to China) were well-remembered and their travelogues not objected to by the Catholic church. The Viking discovery of Vinland (North America) was only remotely remembered; the church did not object to the concept that there were vast bodies of water and land out there yet to be discovered by christian Europeans. Columbus claimed to sail out in order to prove the hypothesis, the earth to be round, wrong (an argumentation designed to outtrick the Inquisition). Arriving in the Caribbean Islands (1492), he referred to the archipelago as the Indies, soon to be known as the West Indies.

48. Zeal.com - United States - New - Library - Sciences - Mathematics - Mathematicia 4. eratosthenes of cyrene http//wwwgroups.dcs.st-and.ac.uk/~history/Mathematicians/E Biography of Eratosthenes, who very accurately measured the http://zeal.com/category/preview.jhtml?cid=572631

49. ERATOSTHENES ERATOSTHENES c.274 c.194 BC Greek Scholar eratosthenes of cyrene studied inAlexandria and Athens. In Alexandria he was director of the great library. http://www.hyperhistory.com/online_n2/people_n2/persons2_n2/eratosthenes.html

ERATOSTHENES c.274 - c.194 BC Greek Scholar Eratosthenes of Cyrene studied in Alexandria and Athens. In Alexandria he was director of the great library. This scholar of natural history did his most outstanding work in mathematics and geography. Eratosthenes calculated the circumference of the earth correctly. This he did by observing the different angle's that the sun's rays fall in two cities 500 miles apart. He correctly assumed the Sun's distance to be so great that the rays are practically parallel when they reach the earth. www link : From the University of St. Andrews, Scotland School of Mathematics Biography

50. Web Links For Chapter 5 http//www.math.utah.edu/~alfeld/Eratosthenes.html (eratosthenes of cyrene).A biographical and portrait of Eratosthenes can be found at. http://www.mhhe.com/math/advmath/rosen/student/webres/ch5links.mhtml

Web Links for Chapter 5 Section 5.1. Recurrence Relations Page 310 A variety of ways that Fibonacci number arise in nature, including counting rabbits, can be found on Ron Knott’s page at the Department of Computing, University of Surrey site: http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html (The Fibonacci Numbers and Golden Section in Nature) To go straight to the rabbits, see http://www.ee.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibrab.html#rab (The Fibonacci Rabbit Sequence) Page 311 A picture of the 19 th century original box cover for the Tower of Hanoi puzzle and the text of the original instructions in French, and translated into English, can be seen at the site of Paul K. Stockmeyer, a professor of computer science at William and Mary College. http://www.cs.wm.edu/~pkstoc/toh.html (Tower of Hanoi) Several interesting papers about the Tower of Hanoi problem and its generalizations written by Paul K. Stockmeyer can be downloaded from http://www.cs.wm.edu/~pkstoc/h_papers.html (Tower of Hanoi Papers) Many Web sites run demonstrations of the Tower of Hanoi puzzle. Some of these demonstrate the moves used to solve the puzzle in an animation. Others run in an interactive mode where you can move disks yourself (by clicking and/or dragging) . Here are some of these sites. (Note: For some of these sites you must have a Java-enabled browser to run the animated and/or interactive programs.)

51. Dyalog APL - Sieve Of Eratosthenes nvec ? .sieve nvec © Sieve of Eratosthenes © eratosthenes of cyrene(¯276¯194) Removes multiples of numbers within the argument vector. http://www.dyalog.com/dfnsdws/n_sieve.htm

nvec „ #. sieve nvec © Sieve of Eratosthenes © Eratosthenes of Cyrene (¯276-¯194) Removes multiples of numbers within the argument vector. Thus sieve 2..¾ returns those primes in the range 2..¾. An illustration of most of the D-function con- structs: left argument defaulting; local definition; guards; tail recursion. Example: sieve 2 to 100 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 See also: to Back to: contents Back to: Dyalog APL

52. Singapore Science Centre ScienceNet Computer Science / IT eratosthenes of cyrene (c275c195 BC) was a Greek philosopher and mathematician.He also was the head of the great library at Alexandria. http://www.science.edu.sg/ssc/detailed.jsp?artid=540&type=6&root=1&parent=1&cat=

53. Expt. II-3 Measuring The Size Of The Earth eratosthenes of cyrene (273192BC) masterfully measured the size of the earth. Eratostheneswas born in Cyrene, the capital city of the region west of Egypt. http://homepage.mac.com/dtrapp/ePhysics.f/labII_3.html

ie-Physics Experiment II-3 Measuring the Size of the Earth If Aristarchos was correct and the Earth did orbit the Sun, then there should be confirming evidence both here on Earth, and with careful observations of the sky. If the Earth moved, the motion would likely be felt. If the Earth moved the motion would likely cause strong prevailing winds from the direction of motion. But more fundamentally, if the Sun occupied the center position and the Earth orbited the Sun, then the angle between neighboring stars along the ecliptic should change with the seasons. When the Earth was closer to the stars the angle should be larger, but when the Earth orbited farther from the stars the angle between the stars should decrease. The lack of any such observable parallax , the lack of any prevailing winds, and the lack of any other evidence of earth motion led the Greeks to reject Aristarchos' proposal that the Earth orbited the Sun. Eratosthenes of Cyrene (273-192BC) masterfully measured the size of the earth. Eratosthenes was born in Cyrene, the capital city of the region west of Egypt. He was educated in Athens, which was still the educational and philosophical center of the Mediterranean despite the rise of the Roman empire. After distinguishing himself academically, he was recruited by the Ptolemaios to tutor a prince in Alexandria, Egypt. Ten years later he became the chief librarian of the Museum of Alexandria, a job that went beyond supervising the vast collections to include leading for four decades the extensive scientific research sponsored by that institution. While he excelled in many areas, Eratosthenes became one of the greatest geographers of all ages by establishing the mathematical geography of the spherical earth.

54. Welcome To Turkey In Maps WORLD ACCORDING TO ERATOSTHENES, c. 194 BC A 19th century reconstructionof the world view of eratosthenes of cyrene (275194 BC). http://turkeyinmaps.com/Sayfa1.html

The Early Maps Mankind, from very early ages, have felt the need of making plans and maps to let each other know the whereabouts of locations of importance to them. Unfortunately, many of these early maps which were unique manuscripts, have not survived to our time. This is why most of the maps in this section are later reconstructions of the originals. I still preferred to include them in this section for they represent the cartographic knowledge of their times. I could not find maps of this period specific to Anatolia. However, the region is shown in most of the early maps being at the centre of the inhabited world Please also see the special sections on Ptolemaic and Medieval maps. Babylonian clay tablet world map, 600 B.C. CATAL HOYUK MAP, Turkey, c. 6,200 BC One of the earliest maps is the one discovered during an excavation in 1963 by James Mellaart in Ankara, Turkey at the archeological site at Catal Hoyuk (pronuonced Chatal Hoeyuek) in central Anatolia. This is a wall painting that is approximately nine feet long. It is believed that the map depicts the town plan of Catal Hoyuk itself. In the foreground is a town arising in graded terraces. Behind the town is an erupting volcano. This is possibly Hasan Dag. For more information please click on the map.

55. The Transit Of Venus And The Quest For The Solar Parallax The Greek astronomer, eratosthenes of cyrene (c276 195 BC), was able to deducethe Earth s radius by means of a strikingly simple set of observations. http://www.dsellers.demon.co.uk/venus/ven_ch1A.htm

T HE T RANSIT OF V ENUS The Quest for the Solar Parallax Now available as a full-length book: Order from Amazon! By David Sellers ( Leeds England Published by MagaVelda Press Almost every High School child knows that the Sun is 93 million miles (or 150 million Kilometres) away from the Earth. Despite the incredible immensity of this figure in comparison with everyday scales - or perhaps even because it is so hard to grasp - astronomical data of this kind is accepted on trust by most educated people. Very few pause to consider how it could be possible to measure such a distance - the 'Astronomical Unit' - and few are aware of the heroic efforts which attended early attempts at measuring it. Unfortunately, even most popular astronomy text books give insufficient information to allow one to see precisely how the task was accomplished. Sizing the Yardstick: the Diameter of the Earth In the history of astronomy, the quest for the Astronomical Unit (AU) has normally been regarded as the quest for a more fundamental quantity: namely, the 'Solar Parallax'. The solar parallax is not a distance at all. It is an angle: the angle subtended at the centre of the Sun by the Earth's radius (see Figure 1 ). If this angle is known and the radius of the Earth can be measured, then the distance to the Sun can be deduced by simple calculation. Clearly, the first piece of information which was needed in order to size the AU was the radius of the Earth.

56. The Alexandrian Library Tables. He was replaced by eratosthenes of cyrene in 235 BCE, a manwho was very knowledgeable in geography and chronology. Ptolemy http://www.richeast.org/htwm/Greeks/library/library.html

The Greeks The Greeks The Romans Other Civilizations Index Mare Nostrum The Alexandrian Library by V. Russell Establishment The Alexandrian Library played an important role throughout history. According to Little (35), it contained the largest collection of wisdom that ever existed. The earliest documentation of the library is in the Letter of Aristeas which describes the legend of seventy translators of the Hebrew Bible that had worked in Alexandria during the reign of Philadelphus (Fraser 320). It was in this city that the library was established. Alexandria was founded by Alexander the Great in 331 BCE. It is located on the northern part of Egypt where the Nile meets the Mediterranean Sea. Alexander's empire stretched from Egypt to Asia. After his death at the age of 32, his empire was divided among several rulers. Ptolemy, a Greek general, made himself pharaoh over all of Egypt. He also made Alexandria the capital of Egypt. Creation The library was created when Demetrius, a former ruler of Greece, suggested to Ptolemy that he should gather books in the style of Plato's philosopher kings on the world's people and on kingship and ruling. Demetrius is also believed to have helped to inspire the founding of the Museum of Alexandria, a temple dedicated to the Muses (Brudige). Most libraries back in the times of the Alexandrian Library were collections of manuscripts owned by private individuals. According to Bevan (125), after Plato's death, most of his library had been passed on to the Alexandrian Library. The fire that destroyed in the library in 48 BCE destroyed much information that may never be known again.

57. AE Connect. A Site Of Comprehensive Links To Ancient Egypt Dam Nubian Museum Aswan Nubian Museum - Aswan Kitchener s Island Eratosthenes well Eratosthenes at Syene - German eratosthenes of cyrene Eratosthenes The http://members.optushome.com.au/fmetrol/egypte/

Last update May 19th 2004 Currently listings this page. This site checked regularly with Xenu Link Sleuth Cairo sites are the most likely to be down at anyone time For example, those beginning with www.sis.gov Other links that may be temporarily down = translate with Babelfish Support the anti counter council Ancient Egypt resources on the WWW desultory alphabetic A ABZU ABZU - Egypt and Sudan - table of contents ABZU - Ancient Near East - browse by author - title ABZU - Archaeological site photography ... ABZU - Breasted expedition ABYDOS Abydos Abydos - French Abydos - Abtu Abydos Egypt - Compass ... The Abydos Egypt Temple Glyphs A Abydos - Survey for Paleolithic sites Ancient Abydos - Archaeology Weni the Elder - Abydos The Archaeology of Individuals at Abydos ... "Magical" Birth Brick Discovered in Abydos news item First plank vessel unearthed - Abydos news item Earliest Royal Boats at Abydos Important archaeological find at Abydos news item Were Egyptians the first Scribes - Abydos news item Abydos, Umm el-Qab - Earliest royal tombs in Egypt

58. Web Diva Club Primes of Life eratosthenes of cyrene lived approximately 275195 BC.He was the first to estimate accurately the diameter of the earth. http://www.girlstart.com/lessons/math/class/lesson4.htm

Primes of Life Eratosthenes of Cyrene lived approximately 275-195 BC. He was the first to estimate accurately the diameter of the earth. He was highly regarded in the ancient world, but unfortunately only fragments of his writing have survived. One of his living contributions is the "Sieve of Eratosthenes," a method for identifying prime numbers. A prime number is a natural number greater than 1 that can be divided without remainder only by itself and by 1. Natural numbers that can be divided by a number less than itself and greater than 1 are composite numbers . Try to identify all prime numbers up to 100 using the "Sieve of Eratosthenes." Choose five different color markers and print out the 100 chart Shade in the number 1 square with the red marker. It is special and unique. Do you know why? Think about this: Is 1 prime? Think about what it means to be prime. We said it was a number that can only be divided by 1 and itself without a remainder. But 1 is itself. Are you confused yet? You should be. This is confusing stuff! It is like defining a word by using the word itself. For example: "blue" is the color that makes blue. Silly isn't it! But that's why we don't consider 1 prime. Now, is 1 a composite? Of course not. The only number that makes up 1 is 1. So, the number 1 is neither prime nor composite. And that's why it's a special number! The number 2 is the first prime number. Shade in all the multiples of 2 with the second marker. What pattern formed by shading all the multiples of two? Straight horizontal lines are formed. It eliminates all even numbers because they are all multiples of two.

59. Rectangular Arrays The problem dates back at least to eratosthenes of cyrene (280 to 194 BCE), the acclaimedscholar and head of the Library at Alexandria in Egypt who wrote the http://www.recoveredscience.com/Primes1ebook01.htm

recoveredscience .com We offer surprises about in our e-book Prime Passages to Paradise by H. PeterAleff Site Contents PRIME PATTERNS Table of Contents Rectangular arrays Twin prime proof Prime facts Prime problems Polygonal numbers ... Reader responses Visit our other Sections: Constants Board Games Astronomy Medicine Store Stuff Home Page Search this site FAQ about e-books Download free e-books ... email us Footnotes : William Poundstone: "Labyrinths of Reason Paradox, Puzzles and the Frailty of Knowledge", Anchor Press, New York, 1988, in chapter on "NP-Completeness" on page 177. Sir Thomas Heath: "A History of Greek Mathematics", Clarendon Press, Oxford, 1921, edition consulted Dover, New York, 1981, Volume 2, page 104. Apollonius’ life dates are not known, but he was famous as an astronomer under Ptolemy Philopator (222 to 205 BCE). See Heath: "A History of Greek Mathematics", op. cit., Volume 2, page 126. Picture credit: Seven- circuit Labyrinth of Cretan type redrawn from Jeff Saward's Caerdroia Journal see our "useful Links" page.

60. Eratosthenes From FOLDOC Recommended Reading PM Fraser, eratosthenes of cyrene (Oxford, 1972).A Dictionary of Philosophical Terms and Names. 200110-29 . http://www.swif.uniba.it/lei/foldop/foldoc.cgi?Eratosthenes

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